(3+z)(3z+8)=0

Solution for (3+z)(3z+8)=0 equation:

Simplifying
(3 + z)(3z + 8) = 0

Reorder the terms:
(3 + z)(8 + 3z) = 0

Multiply (3 + z) * (8 + 3z)
(3(8 + 3z) + z(8 + 3z)) = 0
((8 * 3 + 3z * 3) + z(8 + 3z)) = 0
((24 + 9z) + z(8 + 3z)) = 0
(24 + 9z + (8 * z + 3z * z)) = 0
(24 + 9z + (8z + 3z2)) = 0

Combine like terms: 9z + 8z = 17z
(24 + 17z + 3z2) = 0

Solving
24 + 17z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(8 + 3z) = 0

Subproblem 1
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

Simplifying
z = -3
Subproblem 2
Set the factor '(8 + 3z)' equal to zero and attempt to solve:

Simplifying
8 + 3z = 0

Solving
8 + 3z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + 3z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3z = 0 + -8
3z = 0 + -8

Combine like terms: 0 + -8 = -8
3z = -8

Divide each side by '3'.
z = -2.666666667

Simplifying
z = -2.666666667
Solution
z = {-3, -2.666666667}